Artificial Semiconductor Superlattices and Quantum Well Structures Klaus Ploog, Stuttgart (Max-Planck-lnstitut fur Festkörperforschung)

The recent developments in the thin- monstrate the effect of energy quantiza­ film growth techniques of Molecular tion on the optical and transport proper­ Beam Epitaxy (MBE) and Metalorganic ties. The admixture of Al to the direct- Vapour Phase Epitaxy (MOVPE) make gap semiconductor widens the energy possible the synthesis of highly refined gap of AlxGa1-xAs, but it produces only ultrathin multilayer structures compos­ minor additional distortion because of ed of a periodic array of equally spaced the closely related chemical nature of Al hetero- or homojunctions in crystalline and Ga atoms. This widening raises the semiconductors (Fig. 1). The consti­ conduction band edge and lowers the tuent layer thicknesses Lz and Lb have valence band edge, and thus potential Fig. 2 — (a) Periodic layer sequence of a now been scaled down to atomic barriers for both electrons and holes are GaAs/AlxGa1-xAs superlattice and (b) varia­ monolayers. In these artificial superlat­ created. The band gap discontinuity bet­ tion of the conduction and valence band tices or multi-quantum well (MQW) ween GaAs and AlxGa1-xAs occurs edges. εi, εhhi, and εlhi denote the subband structures, novel physical phenomena mainly in the conduction band. To a good energies. occur arising from quantum size effects. approximation the sub-band structure of quantum well structures can be directly The energies and wavefunctions of elec­ this materials system can be obtained probed by optical absorption measure­ trons and holes are significantly modi­ from simple calculations by wavefunc- ments (Fig. 3). A series of absorption fied as compared to bulk material, and tion matching, using the effective peaks is observed in samples of different quantized energy levels, called sub- or masses m * of the Kronig-Penney model. configuration, owing to transitions from minibands, are formed. The free carriers The quantized energy is h2n2/8m*L2 for conduction sub-bands to valence sub­ are essentially confined in the plane of the n th confined state which contains n bands. The energy levels are shifted the layers and thus become two-dimen­ electron half-wavelengths in a well from the band gap to higher energy be­ sional. Consequently, the density-of- thickness Lz. This value corresponds to cause of size quantization in the GaAs states exhibits a staircase shape with the ideal case of infinitely high barriers, layers. The absorption spectra show step increases at the sub-band edges. but is less for finite barrier heights. For a contributions from both heavy and light In Fig. 1 we show the periodic layer se­ more accurate calculation the allowed holes, and also confirm the selection quence of a GaAs/AlGa1-xAs superlat­ electron and hole states can be deter­ rules of the principal quantum number tice and the periodic variation of the cor­ mined by solving Schrödinger's equa­ Δn = 0 for such transitions. The data of responding conduction and valence tion and matching the wavefunctions to Fig. 3 can be explained by the approxi­ band edges. This prototype superlattice the appropriate boundary conditions. mation that the electrons and holes are represents an ideal system for theoreti­ The existence of quantized states or confined by square-well potentials aris­ cal analysis and for experiments to de­ sub-bands in GaAs/AlxGa1 xAs multi- ing from the heterojunction band dis­ Fig. 1 — Transmission electron micrograph of a (110) cleaved and thinned GaAs/A/As super­ continuities. This simple particle-in-the- lattice of layer thicknesses Lz = Lb = 10 nm. box model accounts for the observed absorption spectra, if we assume that about 85% of the band-gap discontinui­ ty occurs in the conduction band and about 15% in the valence band. It is fur­ ther important to note that the binding energy of an exciton — a bound elec­ tron-hole pair with energy levels in the band gap which moves through the crystal lattice as a unit — is strongly enhanced. This may be factor of four for a 5-nm well, as compared to bulk GaAs, because of the two-dimensional confi­ nement of electrons and holes. As a result, the excitonic features in the ab­ sorption spectra remain stable up to temperatures as high as 300°C. The GaAs/AlxGa1-xAs superlattices and multi-quantum well structures are very attractive for solid state current ex­ cited lasers because light emission based on confined-particle transitions 44 can be tailored to some energy between the band-gap of the GaAs well and that of the AlxGa1-xAs barrier material, sim­ ply by pre-selecting the well thickness and the alloy composition of the barrier during epitaxial growth. While in GaAs bulk material the dominant lumines­ cence arises from electron-to-impurity recombination, the GaAs quantum well luminescence is dominated by intrinsic free-exciton recombination. Moreover, in quantum wells, the electron-hole re­ combination lifetime is reduced signifi­ cantly, owing to carrier localization, so that the luminescence efficiency increa­ ses strongly. In Fig. 4 we show that the high-energy shift of the intrinsic free- exciton luminescence is proportional to the inverse square of the well width Lz. In addition to the blue shift we observe an increasing line width. This is caused by the constant thickness fluctuation within the GaAs quantum well of the Fig. 3 — Absorption spectra of order of one monolayer which has a GaAs/AlxGa 1-xAs multi stronger impact for narrower wells. The quantum well struc­ emission wavelength of GaAs quantum tures with different well lasers can easily be reduced by well widths Lz. The selection of a narrow well width. It is fur­ sample with Lz = 400 ther important to note that in quantum nm shows bulk-type well lasers the density-of-states is modi­ behaviour. fied from the parabolic bulk-like distribu­ tion to a step-like distribution with cons­ tant density-of-states above the band are spatially separated from their parent in a new state, an incompressible elec­ edge up to the next excited sub-band. ionized dopant impurities. The electron tron (or hole) liquid. The excitations of This modification of the density-of-sta­ mobilities in selectively doped GaAs/ this new state are apparently fractional­ tes implies that significantly less carrier AlxGa1-xAs quantum well structures are ly charged quasi-electrons and quasi­ injection is required to reach threshold greatly enhanced as compared to uni­ holes. In addition, a new device concept, for stimulated emission, because in formly doped GaAs, particularly at low called High Electron Mobility Transistor quantum wells more electron states are temperatures (Fig. 6). The reason for the (HEMT) has been developed from these concentrated at energies near the band increased mobilities is the reduction of selectively doped heterostructures for edge. Consequently, extremely low cur­ scattering from ionized dopant impuri­ high-speed logic application. rent threshold densities are observed for ties in the conducting channel, which is quantum well lasers. These new lasers the dominant scattering mechanism at Fig. 4 — Photoluminescence spectra of also hold promise with respect to lasing low temperatures. The ionized impurity GaAs/AlxGa1-xAs quantum well structures lifetime. scattering is further reduced if a thin (5 with different well widths Lz. In selectively doped GaAs/AlxGa, xAs to 25 nm) undoped spacer layer is in­ superlattices and quantum well struc­ serted in the AlxGa1-xAs barrier next to tures, only the wider-gap semiconduc­ the conducting channel. In selectively tor AlxGa1 xAs is doped with either Si n(Si)-doped GaAs/AlxGa1-xAs hetero­ donors or Be acceptors, while the structures with a single interface, low- smaller gap GaAs is left nominally un­ temperature electron mobilities in ex­ doped. Because of the conduction and cess of 2 x 106 cm2/V s have been valence band discontinuity at the achieved. In the complementary selecti­ heterointerface, the free carriers from vely p(Be)-doped heterostructures the the ionized dopant impurities in the low-temperature hole mobilities are in Al Ga1-x As barrier are transferred to the the order of 105 cm2A/ s owing to the adjacent undoped GaAs region where larger effective hole mass. These figures they form a quasi two-dimensional car­ are more than an order of magnitude rier gas. The spatial distribution of the higher than would be found in high puri­ dopant atoms and of the electrons as ty bulk n- and p-type GaAs. well as the relative energy positions of Selective or modulation doping has the band edges, donor levels and elec­ enabled physicists to employ GaAs/ tron levels for a selectively n(Si)-doped AlxGa1- xAs quantum well structures and multi-quantum well structure is shown heterostructures to study totally new schematically in Fig. 5. In this configura­ fundamental problems, including the tion the electrons, which occupy quan­ quantized Hall effect and the ordering of tum well states up to the Fermi level EF the two-dimensional electrons (or holes) 45 (hole) gas systems of selectively doped GaAs/AlxGa, xAs structures: Quantiza­ tion of the Hall resistance to exact ra­ tional fractions of h/e2 occurs at frac­ tional filling of the lowest Landau level. This observation indicates the formation of a new many-particle ground state, an electron (hole) liquid, at these fractional filling factors. Recent theoretical calcu­ lations suggest that this novel electronic state should have unusual properties like fractionally charged quasi-particles and resistance-less conduction at T = 0 K. This fractional quantum Hall effect re­ presents the first observation of a frac­ tional quantum number in physics. In many industrial laboratories exten­ sive effort is now directed towards the development of High Electron Mobility Fig. 5 — (a) Periodic layer sequence of a selectively n(Si)-doped GaAs/AlxGa1-xAs multi Transistors (HEMT) and integrated cir­ quantum well structure and (b) relative energy positions of the band edges, donor levels and cuits made from selectively doped electron levels. GaAs/AlxGa1-xAs quantum well structu­ res. Although the entire low-field mobili­ At low magnetic fields the Hall effect ed by current) is quantized in sub-multi­ ty enhancement is not available in de­ is routinely used to measure carrier con­ ples of h/e2, with e = electron charge vices operating at high electric fields centrations and mobilities in epitaxial and h = Planck's constant. It is impor­ under short gates, the HEMT has shown semiconductor layers. However, if at low tant to note that over a range of more substantially higher speed than uniform­ temperatures high magnetic fields are than 1 kG of applied magnetic field, the ly doped GaAs field effect transistors. In applied perpendicular to the two-dimen­ Hall resistance is constant and reprodu­ Fig. 8 we show the schematic arrange­ sional electron or hole gas in selectively cible to within one part in 108, indepen­ ment of an experimental inverter struc­ doped GaAs/AlxGa1-xAs structures, intri­ dent of the exact geometry of the ture with enhancement-mode switching guing new features develop in the Hall device. This accuracy of quantization HEMT and depletion-mode load HEMT, response and conductivity. As indicated makes the selectively doped Hall struc­ which was first realized by Fujitsu Ltd. in Fig. 7, wide flat plateaux in Hall resis­ tures attractive for a new resistance (Japan). Ring oscillator circuits fabrica­ tance and wide regions of vanishing re­ standard and for determination of the ted with such elements have achieved sistance parallel to the current flow oc­ fine structure constant a, which is propagation delays down to 12 ps at cur under variation of the perpendicular directly proportional to e2/h (Europhys. room temperature and 10 ps at liquid magnetic field. At each of the plateaux, News 16 (1985) 11/12). A behaviour nitrogen temperature (77 K). These are the Hall resistance (i.e. Hall voltage divid- similar to that shown in Fig. 7 is observ­ the highest speeds reported to date for a ed in two-dimensional hole systems. digital circuit. Recently, more realistic The physical reason for the peculiarity high-speed logic circuits based on Fig. 6 — Variation of Hall electron mobility of a two-dimensional electron or hole the two-dimensional quantum confined with temperature in a selectively n(Si)- electron channel in selectively doped doped GaAs/AlxGa1-xAs multi quantum well gas in a strong magnetic field is that the structure. energy spectrum of the electrons (holes) is discrete (formation of Landau levels) Fig. 7 — Variation of Hall resistance and because of orbital quantization of the parallel resistance with magnetic field in a cyclotron motion in a magnetic field. selectively n(Si)-doped GaAs/AlxGa1-xAs Quantization of the Hall resistance to quantum well structure. exact multiples of h/e2 are observed at integer values of Landau level filling. To­ day, the integral quantum Hall effect is interpreted in terms of gaps in the single­ particle density-of-states between Lan­ dau levels. The formation of localized states in the gap region between magne­ tic levels owing to disorder (i.e. random distribution of impurities or interface steps) is assumed to account for the width of the plateaux and the width of the zero-resistance region in Fig. 7. At very low temperatures (< 1K) and high magnetic fields up to 30 T in the ex­ treme quantum limit, where only the lowest Landau level contains carriers, striking new features are observed in high-mobility two-dimensional electron 46 GaAs/AlxGa1-xAs structures have been developed, including flip-flop frequency dividers with a dividing frequency of 5.5 GHz at room temperature and 10.1 GHz Fig. 8 — Schematic at liquid-nitrogen temperature as well as layer arrangement of a 4 kb HEMT SRAM ("Static Random experimental inverter Access Memory") with an address ac­ structure based on cess time of 2.0 ns at liquid-nitrogen High Electron Mobility temperature. Transistor (HEMT).

New Individual Ordinary Members of EPS

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